在python/numpy中计算滚动加权和而不使用for循环

Question

我最近问了一个问题:NumPy卷积方法与当量加权平均价格的循环方法有轻微的差异

尝试使用np.convolve来计算滚动VWAP度量比标准的for循环要快得多，但是提供了一个不正确的计算，因为它省略了数组中的最后一项。

有没有一种方法可以在没有for循环的情况下进行滚动加权和?

我试过了:

使用标准for循环(慢)

def calc_vwap_1(price, volume, period_lookback):
"""
Calculates the volume-weighted average price (VWAP) for a given period of time.
The VWAP is calculated by taking the sum of the product of each price and volume over a given period, 
and dividing by the sum of the volume over that period.

Parameters:
price (numpy.ndarray): A list or array of prices.
volume (numpy.ndarray): A list or array of volumes, corresponding to the prices.
period_lookback (int): The number of days to look back when calculating VWAP.

Returns:
numpy.ndarray: An array of VWAP values, one for each day in the input period.
"""
vwap = np.zeros(len(price))
for i in range(period_lookback, len(price)):
lb = i - period_lookback  # lower bound
ub = i + 1  # upper bound
volume_sum = volume[lb:ub].sum()
if volume_sum > 0:
vwap[i] = (price[lb:ub] * volume[lb:ub]).sum() / volume_sum
else:
vwap[i] = np.nan
return vwap

在same模式下使用np.convolve

def calc_vwap_2(price, volume, period_lookback):
price_volume = price * volume
# Use convolve to get the rolling sum of product of price and volume
price_volume_conv = np.convolve(price_volume, np.ones(period_lookback), mode='same')[period_lookback-1:]
# Use convolve to get the rolling sum of volume
volume_conv = np.convolve(volume, np.ones(period_lookback), mode='same')[period_lookback-1:]
# Create a mask to check if the volume sum is greater than 0
mask = volume_conv > 0
# Initialize the vwap array
vwap = np.zeros(len(price))
# Use the mask to check if volume sum is greater than zero, if it is, proceed with the division and store the result in vwap array, otherwise store NaN
vwap[period_lookback-1:] = np.where(mask, price_volume_conv / volume_conv, np.nan)
return vwap

在valid模式下使用np.convolve

def calc_vwap_3(price, volume, period_lookback):
# Calculate product of price and volume
price_volume = price * volume
# Use convolve to get the rolling sum of product of price and volume and volume array
price_volume_conv = np.convolve(price_volume, np.ones(period_lookback), mode='valid')
# Use convolve to get the rolling sum of volume
volume_conv = np.convolve(volume, np.ones(period_lookback), mode='valid')
# Create a mask to check if the volume sum is greater than 0
mask = volume_conv > 0
# Initialize the vwap array
vwap = np.zeros(len(price))
# Use the mask to check if volume sum is greater than zero, if it is, proceed with the division and store the result in vwap array, otherwise store NaN
vwap[period_lookback-1:] = np.where(mask, price_volume_conv / volume_conv, np.nan)
return vwap

使用np.cumsum(对不起妈妈)与切片

def calc_vwap_4(price, volume, period_lookback):
price_volume = price * volume
# Use cumsum to get the rolling sum of product of price and volume
price_volume_cumsum = np.cumsum(price_volume)[period_lookback-1:]
# Use cumsum to get the rolling sum of volume
volume_cumsum = np.cumsum(volume)[period_lookback-1:]
# Create a mask to check if the volume sum is greater than 0
mask = volume_cumsum > 0
# Initialize the vwap array
vwap = np.zeros(len(price))
# Use the mask to check if volume sum is greater than zero, if it is, proceed with the division and store the result in vwap array, otherwise store NaN
vwap[period_lookback-1:] = np.where(mask, price_volume_cumsum / volume_cumsum, np.nan)
return vwap

使用np.reduceat

def calc_vwap_5(price, volume, period_lookback):
price_volume = price * volume
# Use reduceat to get the rolling sum of product of price and volume
price_volume_cumsum = np.add.reduceat(price_volume, np.arange(0, len(price), period_lookback))[period_lookback-1:]
# Use reduceat to get the rolling sum of volume
volume_cumsum = np.add.reduceat(volume, np.arange(0, len(price), period_lookback))[period_lookback-1:]
# Create a mask to check if the volume sum is greater than 0
mask = volume_cumsum > 0
# Initialize the vwap array
vwap = np.zeros(len(price))
# Use the mask to check if volume sum is greater than zero, if it is, proceed with the division and store the result in vwap array, otherwise store NaN
vwap[period_lookback-1:] = np.where(mask, price_volume_cumsum / volume_cumsum, np.nan)
return vwap

使用np.lib.stride_tricks.as_strided

def calc_vwap_6(price, volume, period_lookback):
price_volume = price * volume
price_volume_strided = np.lib.stride_tricks.as_strided(price_volume, shape=(len(price)-period_lookback+1, period_lookback), strides=(price_volume.strides[0], price_volume.strides[0]))
volume_strided = np.lib.stride_tricks.as_strided(volume, shape=(len(price)-period_lookback+1, period_lookback), strides=(volume.strides[0], volume.strides[0]))
price_volume_sum = price_volume_strided.sum(axis=1)
volume_sum = volume_strided.sum(axis=1)
mask = volume_sum > 0
vwap = np.zeros(len(price))
vwap[period_lookback-1:] = np.where(mask, price_volume_sum / volume_sum, np.nan)
return vwap

测试数据

import numpy as np
price = np.random.random(10000)
volume = np.random.random(10000)
print(calc_vwap(price, volume, 100))
print()
print(calc_vwap_1(price, volume, 100))
print()
print(calc_vwap_2(price, volume, 100))
print()
print(calc_vwap_3(price, volume, 100))
print()
print(calc_vwap_4(price, volume, 100))
print()
print(calc_vwap_5(price, volume, 100))
print()
print(calc_vwap_6(price, volume, 100))
print()

结果

vwap_1 -> [0.         0.         0.         ... 0.47375965 0.47762679 0.48448903] # CORRECT CALCULATION
vwap_2 -> [0.         0.         0.         ... 0.53108759 0.51933363 0.51360848]
vwap_3 -> [0.         0.         0.         ... 0.49834202 0.4984141  0.49845759]
vwap_4 -> [0.         0.         0.         ... 0.49834202 0.4984141  0.49845759]
vwap_5 -> [0.         0.         0.         ... 0.48040529 0.48040529 0.48040529]
vwap_6 -> [0.         0.         0.         ... 0.47027032 0.48009596 0.48040529]

Answer 1

可以这样做:

使用np。同模卷积

def calc_vwap_2(price, volume, period_lookback):
price_volume = price * volume
# Use convolve to get the rolling sum of product of price and volume
if period_lookback%2 == 0:
st = period_lookback//2
en = -period_lookback//2
else:
st = period_lookback//2 + 1
en = -period_lookback//2 + 1
price_volume_conv = np.convolve(price_volume, np.ones(period_lookback+1), mode='same')[st:en]
# Use convolve to get the rolling sum of volume
volume_conv = np.convolve(volume, np.ones(period_lookback+1), mode='same')[st:en]
# Create a mask to check if the volume sum is greater than 0
mask = volume_conv > 0
# Initialize the vwap array
vwap = np.zeros(len(price))
# Use the mask to check if volume sum is greater than zero, if it is, proceed with the division and store the result in vwap array, otherwise store NaN
vwap[period_lookback:] = np.where(mask, price_volume_conv / volume_conv, np.nan)
return vwap
# 1.11 ms ± 26.7 µs per loop (mean ± std. dev. of 3 runs, 100 loops each)

使用np。有效模式下的卷积

def calc_vwap_3(price, volume, period_lookback):
# Calculate product of price and volume
price_volume = price * volume
# Use convolve to get the rolling sum of product of price and volume and volume array
price_volume_conv = np.convolve(price_volume, np.ones(period_lookback+1), mode='valid')
# Use convolve to get the rolling sum of volume
volume_conv = np.convolve(volume, np.ones(period_lookback+1), mode='valid')
# Create a mask to check if the volume sum is greater than 0
mask = volume_conv > 0
# Initialize the vwap array
vwap = np.zeros(len(price))
# Use the mask to check if volume sum is greater than zero, if it is, proceed with the division and store the result in vwap array, otherwise store NaN
vwap[period_lookback:] = np.where(mask, price_volume_conv/volume_conv, np.nan)
return vwap
# 1.22 ms ± 17.5 µs per loop (mean ± std. dev. of 3 runs, 100 loops each)

使用np.ufunc.reduceat

def calc_vwap_5(price, volume, period_lookback):
price_volume = price * volume
# Use reduceat to get the rolling sum of product of price and volume

indices = np.arange(0,len(price)+1)
isz = indices.itemsize
indx = np.lib.stride_tricks.as_strided(indices, shape=(len(price)-period_lookback, 2), strides=(isz, (period_lookback+1)*isz))
price_volume_cumsum = np.add.reduceat(price_volume, indx.ravel()[:-1])[::2]
# Use reduceat to get the rolling sum of volume
volume_cumsum = np.add.reduceat(volume, indx.ravel()[:-1])[::2]
# Create a mask to check if the volume sum is greater than 0
mask = volume_cumsum > 0
# Initialize the vwap array
vwap = np.zeros(len(price))
# Use the mask to check if volume sum is greater than zero, if it is, proceed with the division and store the result in vwap array, otherwise store NaN
vwap[period_lookback:] = np.where(mask, price_volume_cumsum / volume_cumsum, np.nan)
return vwap
# 1.64 ms ± 36.5 µs per loop (mean ± std. dev. of 3 runs, 100 loops each)

使用np.lib.stride_tricks.as_strided

def calc_vwap_6(price, volume, period_lookback):
price_volume = price * volume
s = price_volume.itemsize
price_volume_strided = np.lib.stride_tricks.as_strided(price_volume, shape=(len(price)-period_lookback, period_lookback+1), strides=(s, s))
vs = volume.itemsize
volume_strided = np.lib.stride_tricks.as_strided(volume, shape=(len(price)-period_lookback, period_lookback+1), strides=(vs, vs))
price_volume_sum = price_volume_strided.sum(axis=1)
volume_sum = volume_strided.sum(axis=1)
mask = volume_sum > 0
vwap = np.zeros(len(price))
vwap[period_lookback:] = np.where(mask, price_volume_sum / volume_sum, np.nan)
return vwap
# 1.09 ms ± 46.1 µs per loop (mean ± std. dev. of 3 runs, 100 loops each)

测试数据

price = np.random.random(10)
volume = np.random.random(10)
print(calc_vwap_1(price, volume, 2))
print(calc_vwap_2(price, volume, 2))
print(calc_vwap_3(price, volume, 2))
# print(calc_vwap_4(price, volume, 2))
print(calc_vwap_5(price, volume, 2))
print(calc_vwap_6(price, volume, 2))

结果

vwap_1 ->[0.         0.         0.42407022 0.30592959 0.40199312 0.62537516
0.65380957 0.63246025 0.44962312 0.57632784]
vwap_2 ->[0.         0.         0.42407022 0.30592959 0.40199312 0.62537516
0.65380957 0.63246025 0.44962312 0.57632784]
vwap_3 ->[0.         0.         0.42407022 0.30592959 0.40199312 0.62537516
0.65380957 0.63246025 0.44962312 0.57632784]
vwap_5 ->[0.         0.         0.42407022 0.30592959 0.40199312 0.62537516
0.65380957 0.63246025 0.44962312 0.57632784]
vwap_6 ->[0.         0.         0.42407022 0.30592959 0.40199312 0.62537516
0.65380957 0.63246025 0.44962312 0.57632784]

在每个函数的末尾，我都提到了我在10000个随机数上获得的计时细节，周期回看为100，如op。